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a "Derivative" Function block tells you the rate of change of a signal. An "Integral" function block tells you the total change in signal in a given time.

But your example does not make mathematical sense. You say your signal has a random variation so it takes a random time to go from an arbitrary low point to an arbitrary high point. You cant analyse this kind of information with an INT or DER function (or any other kind of function) until your complete data set is collected and you can then choose your start and end time. There is no sensible way to do this in a PLC.

Using an INT or DER function means your time interval needs to be set before you collect the data, not after.